<p>The detection of edges is only one of many steps in the understanding of images. Further processing necessarily involves grouping operations between contours. We present a representation of edge contours by approximating B-splines and show that such a representation facilitates the extraction of symmetries between contours. Our representation is rich, compact, stable, and does not critically depend on feature extraction. We turn our attention to the detection of three types of symmetries: skew symmetries and parallel symmetries, which have proven to be of great importance in inferring shape from contour, and smooth local symmetries, which have been used for planar shape description. We show that our representation facilitates the computation of these symmetries.</p>